An implicit conservative scheme for coupled heat and mass transfer problems with multiple moving interfaces

A conservative scheme for phase transformations under mixed control of heat and mass transport has been deduced. Based on the conservative formulation of the Stefan condition for isothermal diffusion problems in two-phase systems by Illingworth and Golosnoy (Journal of Computational Physics 209 (2005) 207–225), a scheme for transformations under mixed control of heat and mass transport in systems containing multiple moving interfaces was developed. The scheme is illustrated for a phase bounded by two moving interfaces in cartesian, cylindrical or spherical 1D coordinates and for a fully implicit time discretization. In the limiting cases the scheme reduces to either an isothermal diffusion case or the thermally driven transformation of a pure component, for which good agreement with analytical solutions is obtained. The non-isothermal dissolution of a solid phase in a liquid phase illustrates the scheme under mixed control conditions.